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Flatland: the rest of the story

December 21, 2008 — Deacon Duncan

I’m pleased to see that Anthony Horvath wants to discuss my analysis of his attempt to excuse the contradictions in the Gospel story. Alas, in true Gypsy Curse fashion, he seems to have misunderstood my arguments, and consequently accuses me of having misunderstood him. For instance, I remarked early on that, while Horvath’s announced topic concerned transcendence and immanence, the bulk of his discussion concerned what God can and cannot do, i.e. how transcendence applies to the question of what God can and cannot do. Horvath apparently understood that to mean that I thought transcendence was an entirely separate and unrelated topic, which gives him a license to dismiss my entire argument as the irrelevant consequences of an incorrect analysis.

H. Professor’s failure to see how these two fundamental claims about the nature of the thing under discussion connect to the rest of the argumentation I made is the underlying mistake of both of his posts. That we are talking about an entity that is both transcendent and immanent is absolutely critical to the rest of the argumentation. In fact, H. Professor makes complaints that I already answered- but because he fails to see the relation between these attributes and the rest I said, he fails to recognize them.

The last sentence reveals the second prong of Horvath’s attempt to make my arguments irrelevant: because I considered each of his arguments step by step, pointing out the problems that require further defense, he accuses me of raising objections that he had already answered (in subsequent parts of his post). He apparently did not understand that I was following the flow of his own logic: that there must be a reason why the “God can’t do nonsense” argument does not suffice to end the discussion, and why Horvath feels compelled to seek other solutions. I simply laid out what those unresolved problems are, at the beginning of the discussion, so that we could approach the rest of the discussion with an appropriate background.

There is a lot more I could have said, of course, and I’m grateful to Mr. Horvath for having given me the opportunity to explore this topic further. He raises some interesting points, and clarifies some others, and, if you can bear with me through a longish post, I think we’ll see why his defense of the Gospel actually constitutes a full-fledged concession of defeat, and a retreat into universal agnosticism.

Just so there’s no misunderstanding this time, let’s lay out the core issue here. The apologetic claim being made, and to which I am responding, is this: “We can think of certain circumstances under which things might appear to be contradictory, when in fact they are not contradictory when seen from the perspective of a “higher” dimension or domain.” The implication is that, seen from some “higher plane” (that you and I can’t see from), the contradictions in Christian theology aren’t actually contradictions.

Despite accusing me of misunderstanding him, Horvath agrees that this is indeed the issue we need to deal with.

The purpose of the Flatland example was not to say that this was how we relate to God, but rather to show how the rules of logic can appear to be violated in one case but when taken from a ‘higher’ plane can be perceived as nonetheless sound…

The whole point of the Flatland example was that what might seem to be inconsistent and contradictory may not in fact be so.

By the way, this is actually a fairly ancient rationalization, and all the “immanence this” and “transcendence that” is just to lend an aura of sophistication and intellectualism to the old excuse that “God works in mysterious ways (and therefore doesn’t need to make sense).”

The problem with the Flatland analogy, however, is that the intersection of a sphere with a plane produces no actual or apparent contradiction, even from the Flatlander’s point of view. The sphere that intersects the plane does not produce a circle whose circumference is less than its diameter, or which possesses four corners joined at 90 degree angles, or in any other way violates or conflicts with the laws of 2D geometry. It produces an ordinary circle whose radius varies from zero to n back to zero again, over a certain period of time. No contradiction, hence no basis for Mr. Horvath’s analogy.

I don’t think a sphere is really the best volumetric solid for this particular analogy anyway. Let’s help him out a little by suggesting a more complex shape: a torus. Imagine a torus (donut shape) standing upright (like a car tire) and slowly sinking down into the plane of Flatland until its center lies within the plane. As it moves, it will first form a point, then an ellipse that gradually grows bigger, then the middle of the ellipse (across the minor axis) will begin to narrow into more of an hourglass shape (as the hole in the torus approaches the plane).

At a certain point, the “waist” of the hourglass shape will shrink until it becomes a figure-8: two ellipses touching at their tips. Then the two ellipses will separate and move apart, becoming more and more circular as they get farther apart, until at last they are two perfect circles. Again, no violations or contradictions of any laws of geometry. The curves may be more complex, but neither of the resulting circles have square corners or diameters greater than their circumferences or any such thing.

But now, something strange does happen. A Flatlander approaches and tries to push the two circles together so that they touch again. He can’t do it. Pushing one circle makes the other circle slide away. He checks all around to see if any lines connect the two circles, but they don’t. As far as he can see, there is no connection in all of Flatland between the two circles (and there isn’t), yet the behavior of the two circles is consistently linked, such that the distance between them is constant. From a 3D perspective, it all seems quite natural: the Flatlander is pushing the whole torus, and when one side moves the other side moves as well, because its part of the same torus.

Now, if all we wanted was an excuse to ignore inconsistencies in what men claim about God, we could stop right here. We could use this “mysterious” torus to justify the conclusion that the problems in the Gospel must be the same sort of thing. Of course, that would be taking things backwards: in Flatland, the observations justify concluding the existence of a higher dimension. That’s quite a different thing from mere speculation about a higher dimension being enough to justify assuming that the observations must actually have happened.

Since we don’t care to fall into that particular converse fallacy, let’s think some more about what Flatland tells us. First of all, it tells us that truth is consistent with itself. We may not understand that self-consistency all the time, and perhaps we might not even perceive it, but the self-consistency of the truth transcends and is immanent within all dimensions of reality and all domains of real existence. The two circles don’t seem to have any connection, as far as a Flatlander can see, but the consistency of their behavior reflects the consistency of the truth itself, across n-dimensional space, and allows the mathematically-inclined Flatlander to draw specific and reasonable conclusions about the 3rd dimension.

In fact, the Flatlander can even make some predictions about the behavior of 3D objects in 2D space. For example, if a sphere moves through a plane at a constant speed, producing a circle of varying radius, you can plot the radius of the circle as a function of time and produce a sine wave. If the Flatland scientist observes a number of circles exhibiting this peculiar-yet-predictable pattern of variation, it would be consistent with the predicted variations for a 3D sphere moving through a 2D plane, and the scientist’s hypothesis would have some supporting evidence.

Likewise, if God were a being from a higher dimension and were interacting with this one, we could make similar observations. For example, just as the Flatlander observed that there was a superplanar connection between two apparently unconnected circles, we could observe God’s “super-natural” existence by the connection He would make between believers. Take two believers and isolate them from one another so that God is the only possible avenue of communication between them, then dictate a short text passage to one of them, and have God relay the text to the other. When the other believer writes down the text correctly, we have the same “mysteriously-connected circles” that the Flatlander does, and there’s a reason for us to conclude, if not God, then at least some hitherto undocumented connection.

In fact, we wouldn’t even need to do the experiment, since this commonality would arise as an ordinary matter of course. All God would need to do is not take supernatural measures to prevent us from noticing the mysterious connection that consistently linked believers together in ways that were verifiably more than just the product of ordinary happenstance. And there are any number of other ways in which the transcendent existence of God could and would verifiably manifest itself even in our allegedly inferior plane. But obviously none of these things are actually happening, which is why Mr. Horvath devotes so much effort to building a case for the answers lying in some speculative and inaccessible “higher plane.”

This is a key point, by the way. If the contradictions in Christian theology could be resolved by answers that lay within this realm of existence, Horvath would have no need to seek some “higher” plane in which such answers might possibly exist. He’s not proposing this speculation because God’s behavior can be observed to show a consistent pattern of superdimensionality that would justify a conclusion of divine transendence. He can’t: God does not show up in real life to give us any transcendent behavior to find patterns in. No, the problem is that Christian theology has a number of glaring inconsistencies and contradictions for which there is no resolution in this “dimension,” and that’s why Horvath needs to postulate the existence of some other, higher, and less accessible realm in which such answers might possibly be hiding.

Horvath takes me to task for failing to address his analogy about the relationship between an author and his characters, so let me rectify that omission right now. This, sadly, is a singularly unfortunate argument for him to make, since the God we’re talking about here is one who only shows up (as far as the real world is concerned) as a character in the stories men tell. We are not observing a God who shows up in real life and whose behavior and characteristics are puzzling to our limited minds. All we can observe in real life is that men tell us things about God that are inconsistent both with themselves and with objective reality.

Horvath himself is participating in the story-building that props up the Gospel. He’s taking the story as it has been told so far, and is using his imagination to try and come up with some kind of scenario that will make the story sound more plausible. If you’ve ever participated in any kind of group fiction-writing (or role play, which can be very similar), you know that this is exactly how fiction is produced. Just imagine something, and if it sounds plausible, add it to the story, and make the story better. That’s how you make a story get better over time, and coincidentally, it’s a theologian’s job description as well.

Trying to patch up the holes in the Gospel, though, only serves to demonstrate that the Gospel does indeed have holes. And that’s the fatal flaw in Horvath’s argument by analogy. When a person creates a story, they’re not creating reality, they’re manipulating abstracted concepts about reality, in ways that may or may not reflect some of the perfect self-consistency of genuine truth. Ultimately, though, all fiction fails at some point to be as consistent with real-world truth as real-world truth is with itself. When humans imagine a story, therefore, what they are doing is not analogous to creating a genuine reality.

In other words, Horvath’s analogy is false, because fiction writing fails to parallel reality at the point where it needs to be strictly parallel in order to be valid. The real world is not merely less self-contradictory that fiction, it is non-self-contradictory. You cannot correctly use the discrepancies between fiction and reality to argue for a corresponding discrepancy between reality and some supposed “higher” plane, because reality doesn’t have the inconsistencies and contradictions that define what it means to be fiction.

Horvath would like to argue otherwise, but my goodness, I’m over 2K words already, and there’s still a bunch of misconceptions and misdirections that I need to correct! I’d better split this into two parts and come back for more tomorrow.

6 Responses to “Flatland: the rest of the story”

“Of course, that would be taking things backwards: in Flatland, the observations justify concluding the existence of a higher dimension. That’s quite a different thing from mere speculation about a higher dimension being enough to justify assuming that the observations must actually have happened.”

That’s a wonderful microcosmic analogy of what’s going on here in the real world with religious apologetics — there is, at the bottom, just a persistent failure to comprehend the empirical perspective and how it differentiates knowledge from fantasy.

Nice job; can’t wait for pt. 2. I read Rudy Rucker’s take on Flatland years ago, and the thing that’s always bothered me, especially in trying to relate some ‘higher’ reality via Flatland analogies, is that I can’t see how a two-dimensional world could actually exist. It seems to me that at best, a two-dimensional existence can only be represented in the abstract. Keep rubbing down the thickness of a chalk line, and the line disappears just at the point where you would have actually achieved true two-dimensionality. Rucker tried to get around the problem by positing a quantum ‘thickness’ which supposedly retained Flatland’s dimensional integrity, but it all seemed a little too facile ala Star Trek ‘science miracles’ to me.

I think this weakens Horvath’s argument even further, since his example of God’s transcending this reality is based on an abstract model that’s probably a real world impossibility. I guess one could also argue that God’s power to sustain the universe is analogous to the way giant invisible turtles hold up the earth. Oh, so THAT’S how it works! * nods head affirmatively*

At heart, the Flatland scenario, whether with sphere or torus, is a false analogy when applied to an internally inconsistent Gospel. The Flatland scenario tells of a phenomena which contradicts the *preconceptions* of the Flatlanders – the phenomena is not itself nonsensical or absurd, albeit is mysterious to the 2D inhabitants. For the situation to be analogous to the Gospels, we would only have to be observing mere mystery in the scriptures, not blatant self-contradiction. Mystery and self-contradiction are simply not analogous.

So I’m totally late to the discussion here, and quite honestly had never heard any Flatland analogy before. Quite interesting. I like how the post forced me to think visually, about the torus and all. Discussions over Bible contradictions are usually best handled separately, IMO, but it seems to me that particular allegation of contradiction X, Y, or Z is not necessarily what’s on trial here, right?

Correct me if I’m wrong, but is the argument on trial here, “We can think of certain circumstances under which things might appear to be contradictory, when in fact they are not contradictory…” (I omitted the ‘higher planes’ part on purpose, BTW, for it’s irrelevant to where I’m going)

I guess all I really want to ask are these, and to Deacon: Are you arguing that error is an intrinsic property of contradiction? Are you arguing that 100% true testimonies cannot contain any contradictions by nature? Furthermore, I define contradiction as the presence of propositions that when taken together form logical inverses of one another. In other words, a contradiction occurs when we state that (x) = (-x).

Just wanted y’all to know what I mean when I use the word contradiction, before I start trying to talk about whether or not they exist and their potential implications. 🙂

I think that, if anything, this flatlanders example is a good illustration of the power of a good scientific theory — the explanation (a sphere) takes up much less bulk of description than the circles.

And I’ve noticed that Xian apologists have a certain fondness for arguing by analogy. And I have a speculation about it that I will concede seems like a rather cynical conspiracy theory: that it is easier to hide bad arguments that way.